Biomedical Engineering Reference
In-Depth Information
Step 2:
Model estimation
T
T
1.
2.
Estimate the kinematic dynamics of the system model
F
=
(
E
[
x
x
])
-
1
E
[
x
x
]
k
- -
1
k
1
k
-
1
k
For each neuron
j
, estimate the tuning function
j
T
•
Linear model
k
=
(
E
[
x
x
])
-
1
E
x
[ ]
x
j
|spike
p
(spike ,
j
k
j
×
x
)
j
•
Nonlinear function
f
j
(
k
× =
x
)
t
j
x
Build the inhomogeneous Poisson generator.
p k
(
×
)
•
Step 3:
Monte Carlo sequential kinematics estimation
i
x
are generated,
i=
1:
N
For each time
k
, a set of samples for state
i
i
1.
2.
Predict new state samples
x
= +
F
x
h
,
i =
1
:N
k
k
k
k
For each neuron
j
,
j
i
i
,
j
j
•
•
Estimate the conditional firing rate
l
=
f
(
k
×
x
)
,
i
= 1:
N
k
k
i
,
j
j
i
,
j
Update the weights
w
µ D
p
(
N
|
l
)
,
i
= 1:
N
k
k
t
Draw the weight for the joint posterior density
=
Õ
,
i
i
j
3.
4.
W
w
,
i
=1:
N
k
k
i
W
j
i
Normalize the weights
=
W
k
,
i
= 1:
N
å
k
W
i
k
N
i
å
i
5.
6.
7.
Draw the joint posterior density
i
p
(
x
|
N
)
»
W
× -
k
(
x
x
)
k
k
k
1:
k
k
i
=
1
*
x
from the joint posterior density by MLE or expectation.
Estimate the state
i
x
according to the weights
i
k
Resample
W
.
6.4.5 decoding Results Using Monte Carlo Sequential Estimation
The Monte Carlo sequential estimation framework was tested for the 2D control of a computer
cursor. In the preprocessing step we consider a dataset consisting of 185 neurons. Here the state vec-
tor is chosen as the instantaneous kinematic vector
=
[
x p v a p v a
to be reconstructed
directly from the spike trains. The position, velocity, and acceleration are all included in the vector
to allow the possibility of sampling different neurons that represent particular aspects of the kine-
matics. Picking only the velocity, for example, might provide only partial information between the
neural spikes and other kinematics. For each neuron in the ensemble, a small time interval of 10
msec was selected to construct the point process observation sequence. With this interval, 99.62%
of windows had a spike count less than 2. For each neuron, 1 was assigned when there was one spike
or more appearing during the interval, otherwise 0 was assigned.
]
T
x
x
y
y
x
y
